I recently purchased the entirety of Fizban's Treasury for character-building purposes on DNDB, with the intent on selecting a gem dragonborn race equivalent that would fit a character that has labradorite scales. However, every time I try to go back and alter the character's dragonborn race, the only variant colors available are the chromatic and metallic dragonborn. Are the gem race features yet to be uploaded/updated to the character builder, or did I miss something?

Try syncing your entitlements. You can click on the link in my signature. And since you are on that page, try checking your licenses too to make sure you purchased the entirety of the book and not just a few races. If that does not work, also try logging out and back in and see if that helps.

I can select gem dragonborns just fine, so the only thing I can think of is the system not having your entitlements in sync.

Ahh--wait, I figured it out. I had to select the "Change Race" option and then go to the variant.